nash 0.1.1

Solving Nash Equilibrium Mixed Strategies
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52

use std::ops::{Add, Sub};

use num::{One, Zero};

use crate::Number;

/// When A has 4 strategies and B has 4 strategies
///
/// Then the payoff matrix for A is `[[a1, a2], [a3, a4]]` and for B is `[[b1, b2], [b3, b4]]`.
///
/// This function returns the mixed strategies for A and B.
pub fn mixed_strategies_4_4(a: &[Number; 4], b: &[Number; 4]) -> ([Number; 2], [Number; 2]) {
    (player_a(a), player_b(b))
}

fn player_a(a: &[Number; 4]) -> [Number; 2] {
    // (a4 - a2) / (a1 - a2 - a3 + a4)
    let [a1, a2, a3, a4] = a;
    let denominator = a1.sub(a2).sub(a3.clone()).add(a4);
    if denominator.is_zero() {
        //
        if a1 == a2 && a3 == a4 {
            return [Number::fraction(1, 2), Number::fraction(1, 2)];
        }
        //
        else if a1 == a2 && a3 < a4 {
            return [Number::one(), Number::zero()];
        }
        //
        else if a1 < a2 && a3 == a4 {
            return [Number::zero(), Number::one()];
        }
        //
        else if a1.sub(a2) == a4.sub(a3) {
            return [Number::fraction(1, 2), Number::fraction(1, 2)];
        }
        else {
            panic!("Invalid payoff matrix: {:?}", a);
        }
    }
    else {
        let p1 = (a4.sub(a2)) / denominator.clone();
        let p2 = (a1.sub(a3)) / denominator.clone();
        return [p1, p2];
    }
}

fn player_b(b: &[Number; 4]) -> [Number; 2] {
    // (a4 - a2) / (a1 - a2 - a3 + a4)
    let [b1, b2, b3, b4] = b.clone();
    player_a(&[b1, b3, b2, b4])
}